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Re: If |2x - 7| > 17, which of the following must be true ................
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31 Oct 2018, 03:49

If |x| > a

Then x > a if x > 0Or -x > a if x< 0 i.e x < -a

Back to the question|2x - 7| > 17

2x-7 > 17 If x > 7/2Or 2x-7 < -17

Solving gives x > 12 or x < -5.

D is the answer.
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Sometimes, the quickest solution to this kind of question involves testing the answer choices

Scan the answer choicesNotice that some answer choices say that x = 1 is a solution, and some say x = 1 is NOT a solution. So, let's test x = 1Plug it into the original inequality to get:|2(1) - 7| > 17Simplify to get: |-5| > 17NOT trueSo, x = 1 is NOT a solution to the inequality. We can ELIMINATE B and C because they say that x = 1 IS a solution.

Scan the remaining answer choicesNotice that some answer choices say that x = -1 is a solution, and some say x = -1 is NOT a solution. So, let's test x = -1Plug it into the original inequality to get:|2(-1) - 7| > 17Simplify to get: |-9| > 17NOT trueSo, x = -1 is NOT a solution to the inequality. We can ELIMINATE A because it says x = -1 IS a solution.

We're down to answer choices D or E. E says x = 6 is a solution, and D says x = 6 is NOT a solution. So, let's test x = 6Plug it into the original inequality to get:|2(6) - 7| > 17Simplify to get: |5| > 17NOT trueWe can ELIMINATE E because it says x = 6 IS a solution.

Answer: D

NOTE: With this particular question, testing the answer choices is a slower approach. However, when solving questions of this nature, the approach is still worth considering, especially with more complex inequalities.